TI-80

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TI-80GRAPHING CALCULATOR

GUIDEBOOK

TI-GRAPH LINK, Calculator-Based Laboratory, CBL, CBL 2, Calculator-Based Ranger, CBR,

Constant Memory, Automatic Power Down, APD, and EOS are trademarks of Texas

Instruments Incorporated.

Windows is a registered trademark of Microsoft Corporation.

Macintosh is a registered trademark of Apple Computer, Inc.

19951997, 2001by Texas Instruments Incorporated.

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Texas Instruments makes no warranty, either expressed or

implied, including but not limited to any implied warranties of

merchantability and fitness for a particular purpose, regarding any

programs or book materials and makes such materials available

solely on an as-is basis.

In no event shall Texas Instruments be liable to anyone for

special, collateral, incidental, or consequential damages in

connection with or arising out of the purchase or use of these

materials, and the sole and exclusive liability of Texas

Instruments, regardless of the form of action, shall not exceed the

purchase price of this calculator. Moreover, Texas Instruments

shall not be liable for any claim of any kind whatsoever against

the use of these materials by any other party.

This equipment has been tested and found to comply with the

limits for a Class B digital device, pursuant to Part 15 of the FCC

rules. These limits are designed to provide reasonable protection

against harmful interference in a residential installation. This

equipment generates, uses, and can radiate radio frequency

energy and, if not installed and used in accordance with the

instructions, may cause harmful interference with radio

communications. However, there is no guarantee that interference

will not occur in a particular installation.

If this equipment does cause harmful interference to radio or

television reception, which can be determined by turning the

equipment off and on, you can try to correct the interference by

one or more of the following measures:

Reorient or relocate the receiving antenna.

Increase the separation between the equipment and receiver.

Connect the equipment into an outlet on a circuit different

from that to which the receiver is connected.

Consult the dealer or an experienced radio/television

technician for help.

Caution: Any changes or modifications to this equipment not

expressly approved by Texas Instruments may void your authority

to operate the equipment.

Important

US FCC

Information

Concerning

Radio Frequency

Interference

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Introduction iii

This manual describes how to use the TI.80 Graphing Calculator. Getting Startedgives a quick overview of its features. The first chapter gives generalinstructions on operating the TI.80. Other chapters describe its interactivefeatures. The applications in Chapter 11 show how to use these featurestogether.

Using this Guidebook Effectively.................... viii

Glossary ......................................... xii

TI-80 Keyboard ................................... 2First Steps ....................................... 3

TI-80 Menus...................................... 4Entering a Calculation: Compound Interest........... 5

Continuing a Calculation........................... 6

Defining a Function: Box with Lid ................... 7Defining a Table of Values.......................... 8

Zooming In on the Table ........................... 9

Changing the Viewing Window...................... 11

Displaying and Tracing the Graph ................... 12

Zooming In on the Graph........................... 13

Other TI-80 Features .............................. 14

Turning the TI-80 On and Off....................... 1-2Setting the Display Contrast ........................ 1-3The Display ...................................... 1-4Entering Expressions and Instructions............... 1-6The Edit Keys .................................... 1-8Setting Modes .................................... 1-9TI-80 Modes...................................... 1-10Variable Names................................... 1-12Storing and Recalling Variable Values................ 1-13Last Entry........................................ 1-14

Last Answer......................................

1-16TI-80 Menus...................................... 1-17The VARS and Y-VARS Menus...................... 1-19EOS (Equation Operating System) .................. 1-20Error Conditions ................................. 1-22

Table of Contents

Getting Started:

Do This First!

Chapter 1:

Operating theTI-80

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iv Introduction

Getting Started: Lottery Chances .................... 2-2Using the TI-80 Functions.......................... 2-3Keyboard Math Operations ......................... 2-4MATH MATH Operations ........................... 2-7

MATH NUM (Number) Operations...................

2-10MATH PRB (Probability) Operations................. 2-12ANGLE Operations................................ 2-14TEST (Relational) Operations....................... 2-16

Getting Started: Working with Fractions ............. 3-2Setting Modes for Fraction Results .................. 3-4Entering and Using Fractions in Calculations ......... 3-6The FRACTION Menu.............................. 3-8

Getting Started: Graphing a Circle................... 4-2Defining a Graph.................................. 4-3Setting Graph Modes .............................. 4-4Defining Functions in the Y= List.................... 4-5Evaluating Y= Functions in Expressions ............. 4-7Selecting Functions ............................... 4-8Defining the Viewing Window ...................... 4-9Displaying a Graph ................................ 4-11Exploring a Graph with the Free-Moving Cursor ...... 4-12

Exploring a Graph with TRACE ..................... 4-13Exploring a Graph with ZOOM...................... 4-15Setting the Zoom Factors .......................... 4-18

Getting Started: Path of a Ball ...................... 5-2Defining and Displaying a Parametric Graph.......... 5-3Exploring a Parametric Graph ...................... 5-6

Chapter 2:

Math, Angle, and

Test Operations

Chapter 3:

Fractions

Chapter 4:

Function

Graphing

Chapter 5:

Parametric

Graphing

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Introduction v

Getting Started: Roots of a Function................. 6-2Defining the Independent Variable .................. 6-3Defining the Dependent Variable .................... 6-4Displaying the Table............................... 6-5

Getting Started: Shading a Graph.................... 7-2DRAW DRAW Menu ............................... 7-3Drawing Lines .................................... 7-4Drawing Horizontal and Vertical Lines ............... 7-5Drawing a Function ............................... 7-6Shading Areas on a Graph.......................... 7-7Drawing Points ................................... 7-10Clearing a Drawing................................ 7-12

Getting Started: Generating a Sequence .............. 8-2About Lists....................................... 8-3LIST OPS Operations.............................. 8-6LIST MATH Operations ............................ 8-9

Getting Started: Building Height and City Size......... 9-2Setting Up a Statistical Analysis..................... 9-8The STAT List Editor.............................. 9-9

Viewing, Entering, and Editing Lists ................. 9-10Sorting and Clearing Lists .......................... 9-13Statistical Analysis ................................ 9-14Types of Statistical Analysis ........................ 9-15Statistical Variables ............................... 9-17Statistical Plotting ................................ 9-18Statistical Analysis in a Program .................... 9-22Statistical Plotting in a Program..................... 9-23

Chapter 6:

Tables

Chapter 7:

Draw Operations

Chapter 8:

Lists

Chapter 9:

Statistics

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vi Introduction

Getting Started: Rolling a Die ....................... 10-2About TI-80 Programs ............................. 10-4Creating and Executing Programs ................... 10-5Editing Programs ................................. 10-6

PRGM CTL (Control) Instructions...................

10-7PRGM I/O (Input/Output) Instructions ............... 10-11Calling Other Programs ............................ 10-14

Probability Experiments: Coins, Dice, and Spinners ... 11-2The Unit Circle and Trigonometric Curves............ 11-3Program: Newtons Numerical Solve Routine ......... 11-4Program: Numerical Integration..................... 11-6Program: Window Variables Store and Recall ......... 11-8

Graphing the Inverse of a Function..................

11-10Graphing a Piecewise Function ..................... 11-12Graphing Inequalities.............................. 11-14Graphing a Polar Equation ......................... 11-15Program: Guess the Coefficients .................... 11-16

Checking Available Memory ........................ 12-2Deleting Items from Memory ....................... 12-3Resetting the TI-80 ................................ 12-4

Chapter 10:

Programming

Chapter 11:

Applications

Chapter 12:

Memory

Management

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Introduction vii

Table of TI-80 Functions and Instructions ............ A-2Menu Map........................................ A-20TI-80 Variables ................................... A-26

Battery Information ............................... B-2Accuracy Information ............................. B-8In Case of Difficulty ............................... B-10Service and Support Information ................... B-14Warranty Information.............................. B-15

Appendix A:

Tables and

Reference

Information

Appendix B:Service and

Warranty

Information

Index

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viii Introduction

The structure of the TI-80 guidebook and the design of its pages can help youfind the information you need quickly. Consistent presentation techniques areused throughout to make the guidebook easy to use.

The guidebook is designed to teach you how to use the

calculator.

Getting Started is a fast-paced, keystroke-by-keystrokeintroduction.

Chapter 1 describes general operation and lays thefoundation for Chapters 2 through 10, which describe

specific functional areas of the TI-80. Most chapters beginwith a brief Getting Started introduction.

Chapter 11 contains application examples that incorporatefeatures from different functional areas of the calculator.These examples can help you see how different functional

areas work together to accomplish meaningful tasks.

Chapter 12 describes memory management.

When possible, units of information are presented on a single

page or on two facing pages. Several page-design elements

help you find information quickly.

Page headingsThe descriptive heading at the top of thepage or two-page unit identifies the subject of the unit.

General textJust below the page heading, a shortsection of bold text provides general information about

the subject covered in the unit.

Left-column subheadingsEach subheading identifies aspecific topic or task related to the page or unit subject.

Using this Guidebook Effectively

Structure of the

Guidebook

Page-Design

Conventions

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Introduction ix

Specific textThe text to the right of a subheadingpresents detailed information about that specific topic or

task. The information may be presented as paragraphs,

numbered procedures, bulleted lists, or illustrations.

Page footersThe bottom of each page shows thechapter name, chapter number, and page number.

Several conventions are used to present information concisely

and in an easily referenced format.

Numbered proceduresA procedure is a sequence ofsteps that performs a task. In this guidebook, each step is

numbered in the order in which it is performed. No other

text in the guidebook is numbered; therefore, when you

see numbered text, you know you should perform thesteps sequentially.

Lists with bulletsIf several items have equalimportance, or if you may choose one of several

alternative actions, this guidebook precedes each item

with a bullet () to highlight itlike this list.

Tables and chartsSets of related information arepresented in tables or charts for quick reference.

Keystroke examplesThe Getting Started examplesprovide keystroke-by-keystroke instructions, as do the

numerous short examples and several detailed examples

that are identified with a.

Information-

Mapping

Conventions

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x Introduction

Several techniques have been used to help you look up

specific information when you need it. These include:

A chapter table of contents on the first page of eachchapter, as well as the full table of contents at the front of

the guidebook.

A glossary at the end of this section, defining importantterms used throughout the guidebook.

An alphabetical table of functions and instructions inAppendix A, showing their correct formats, how to access

them, and page references for more information.

Information about system variables in Appendix A.

A table of error messages in Appendix B, showing themessages and their meanings and giving problem-handling

information.

An alphabetical index at the back of the guidebook, listingtasks and topics you may need to look up.

Reference Aids

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Introduction xi

This glossary provides definitions for important terms that are used throughoutthis guidebook.

An argument is an input upon which the value of a function

depends.

A command is any entry submitted to the calculator using

. There are two types of TI-80 commands: instructionsand expressions.

An expression is a complete sequence of numbers, variables,

functions, and their arguments that can be evaluated to a

single answer. An expression returns the evaluated result to

ANS.

A function, which may have arguments, returns a value andcan be used in an expression.

A function is also the expression entered in the Y= editor used

in graphing.

The Home screen is the primary screen of the TI-80, whereexpressions can be entered and evaluated and instructions

can be entered and executed.

An instruction, which may have arguments, initiates an action.

Instructions are not valid in expressions. An instruction doesnot return a value to ANS.

A list is a set of values that the TI-80 can use for activitiessuch as evaluating a function at multiple values and entering

statistical data.

Menu items are shown on full-screen menus.

Glossary

Argument

Command

Expression

Function

Home Screen

Instruction

List

Menu Items

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xii Introduction

A pixel (picture element) is a square dot on the TI-80 display.The TI-80 display is 64 pixels wide and 48 pixels high.

On the TI-80, real numbers are individual decimal or fractionvalues.

A value is a single decimal or fraction number or a list of

decimals or fractions.

A variable is the name given to a location in memory in which

a value, an expression, a list, or another named item is stored.

Pixel

Real Number

Value

Variable

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Getting Started 1

Getting Started contains two keystroke-by-keystroke examplesan interest rateproblem and a volume problemwhich introduce you to some principaloperating and graphing features of the TI.80. You will learn to use the TI.80 morequickly by completing both of these examples first.

TI-80 Keyboard ................................... 2First Steps ....................................... 3

TI-80 Menus...................................... 4

Entering a Calculation: Compound Interest........... 5

Continuing a Calculation........................... 6

Defining a Function: Box with Lid ................... 7

Defining a Table of Values.......................... 8

Zooming In on the Table ........................... 9

Changing the Viewing Window...................... 11

Displaying and Tracing the Graph...................

12Zooming In on the Graph........................... 13

Other TI-80 Features .............................. 14

Getting Started: Do This First!

Contents

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2 Getting Started

The keys on the TI.80 are grouped by color and physical layout to allow easylocation of the key you need. The keys are divided into zones: graphing keys,editing keys, advanced function keys, and scientific calculator keys.

Graphing &

Editing &

Advanced &Functions

Scientific &Calculator

These keys are most frequently used to access the interactive

graphing features of the TI-80.

These keys are most frequently used for editing expressions

and values.

These keys are most frequently used to access the advanced

functions of the TI-80.

These keys are most frequently used to access the capabilities

of a standard scientific calculator.

TI-80 Keyboard

The Zones of the

Keyboard

Graphing Keys

Editing Keys

Advanced

Function Keys

Scientific

Calculator Keys

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Getting Started 3

Before beginning the two sample problems, follow the steps on this page toreset the TI-80 to its factory settings. (Resetting the TI-80 erases all previouslyentered data.) This ensures that following the keystrokes in this sectionproduces the same actions.

1. Press to turn the calculator on.

If the screen is very dark or blank, adjust the display

contrast. Press and release2, and then press andhold8 (to make the display lighter) or press andhold7 (to make the display darker). You can pressM to clear the display.

E

x

2. Press and release2, and then press. (Pressing2 gives you access to the 2nd operations, which are

printed at the upper left of the keys.MEM is the2nd operation of the key.)

The MEMORYmenu is displayed.

3. Press 3 to select RESET... from the MEMORY menu.

The MEMORY RESET menu is displayed.

4. Press 2 to select RESET from the MEMORY RESET

menu. The calculator is reset, and the

MEM CLEARED message is displayed.

First Steps

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4 Getting Started

To leave the keyboard uncluttered, the TI.80 uses full-screen menus to displaymany additional operations. The use of specific menus is described in theappropriate chapters.

Displaying a Menu

When you press a key that displays a menu, such as

I, that menu screen temporarily replaces the screenwhere you are working.

After you make a selection from a menu, you usually are

returned to the screen where you were.

Moving from One Menu to Another

A menu key may display more than one menu name. Thenames appear on the top line. The name of current menu

is highlighted, and the items in that menu are displayed.

Use9 or6 to display a different menu.

Selecting an Item from a Menu

The number of the current item is highlighted. If there are

more than seven items on the menu, a$ appears on thelast line in place of the : (colon).

To select from a menu, you can either:

Use8 and7 to move the cursor to the item, andthen press.

Press the number of the item.

Note: The tenth item in a menu is number0. If there are

more than 10 items, they are numbered A, B, C, etc. To

select one of these items, press? and then theletter.

Leaving without Making a Selection

To leave a menu without making a selection:

Press2. to return to the Home screen.

PressM to return to the screen where youwere.

Press the key for another screen or menu.

TI-80 Menus

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Getting Started 5

The TI.80 displays up to 8 16-characters lines so that you see an expression andits solution together. You can store values to variables, enter multipleinstructions on one line, and recall previous entries.

Using trial and error, determine when an amount invested at 6% annual

compounded interest will double in value.

1. For the first guess, compute the amount available at

the end of 10 years. Enter the expression just as you

would write it. (Use 1000 for the amount.)

Press 1000p1.06Z10.

2. Press to evaluate the expression.

The answer is shown on the right side of the display.

The cursor is positioned on the next line, ready for

you to enter the next expression.

3. The next guess should be greater than 10 years. Makethe next guess 12 years. To calculate the amount after

12 years, press 1000p1.06Z12, followed by.

Entering a Calculation: Compound Interest

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6 Getting Started

To save keystrokes, you can use the Last Entry feature to recall the lastexpression entered and then edit it for a new calculation. In addition, the nextexpression can be continued from the previous result.

1. The next guess should be less than, but close to, 12

years. Compute the amount available at the end of

11.9 years, using the Last Entry feature. Press2,followed by (the second function of).

The last calculated expression is shown on the next

line of the display. The cursor is positioned at the end

of the expression.

2. You can edit the expression. Press6 to move thecursor over the2. Then type 1.9 to change 12 to 11.9.

Press to evaluate the expression.

Note: This process can be continued to obtain a

solution with the desired accuracy.

3. You can continue a calculation using the result of the

last calculation. For example, if the final amount

determined above is to be divided among seven

people, how much would each person get?

To divide the last calculation by seven, presse7,followed by.

As soon as you presse, ANS is displayed at thebeginning of the new expression. ANS is a variable

that contains the last calculated result. In this case,

ANS contains 2000.505716.

Continuing a Calculation

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Getting Started 7

Take an 8"11" sheet of paper and cut X by X squares from two corners and Xby (X+B) rectangles from the other two corners. Now fold the paper into a boxwith lid. What X would give the maximum volume V of a box made in this way?Use tables and graphs to determine the solution.

Begin by defining a function that describes thevolume of the box.

From the diagram: 2X + A = W

2X + 2B = L

V = A B X

Substituting: V = (W 2X) (L 2 X) X

W

X

X

A

B X B

L

If necessary, pressz to change the

MODE to FLOAT. Then pressy. toreturn to the Home screen and clear it.

1. Press 8.5W to store the width ofthe paper.

Press 11L to store the length ofthe paper.

2. You define functions for tables and graphs on the Y=edit screen.

Presso to access this screen.

3. Enter the function for volume as Y1. PressW2@L2@@to define function Y1 in terms ofX. (@ lets you

enterX quickly without pressing.)

The =sign is highlighted to show that Y1 is selected.

Defining a Function: Box with Lid

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8 Getting Started

The table feature of the TI.80 provides numeric information about a function.Use a table of values from the previously defined function to estimate an answerto the problem.

1. Pressy# (abovep) to display theTABLE SETUP screen.

2. Press to accept TBLMIN=0.

3. Press .5 to define the table increment @TBL=.5.

4. Pressy& (aboves) to display the table.

Note that the maximum value is around 1.5, between

1 and 2.

5. Press and hold to scroll the table until the signchange appears. Note that the maximum length ofX

for this problem occurs where the sign ofY1

(volume) becomes negative.

6. Pressy#. Note that TBLMIN has changed toreflect the first line of the table you last displayed.

Defining a Table of Values

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Getting Started 9

You can adjust the way a table is displayed to get more detailed informationabout any defined function. By varying the value of @TBL, you can zoom in onthe table.

1. Adjust the table setup to get a more accurate

estimate of the maximum size of the cutout. Press 1

to set TBLMIN. Press .1 to set @Tbl.

2. Pressy&.

3. Use and} to scroll the table. Note that themaximum value displayed is 33.072, which occurs at

X=1.6. The maximum occurs at 1.5

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10 Getting Started

4. Pressy#. Press 1.5 to set TBLMIN.Press .01 to set @TBL.

5. Pressy& and use and} to scroll the table.Two equal maximum values are shown, 33.074 at

X=1.58 and X=1.59.

6. Press

or}

to move the cursor to 1.58. Press~

tomove the cursor into the Y1 column. The bottom line

of the display shows the value ofY1 at 1.58 in full

precision, 33.073824.

7. Press to display the other maximum. The valueofY1 at 1.59 in full precision is 33.073908. This

would be the maximum volume of the box if you

could cut your piece of paper at .01-inch increments.

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Getting Started 11

The viewing window defines the portion of the coordinate plane that appears inthe display. The values of the Window variables determine the size of theviewing window. You can view and change these values.

1. Pressp to display the Window variables editscreen. You can view and edit the values of the

Window variables here.

The standard Window variables define the viewing

window as shown. XMIN, XMAX, YMIN, and YMAX

define the boundaries of the display. XSCL and YSCL

define the distance between tick marks on theX

and

Y axes.XMAX

YMIN

YMAX

XSCL

YSCL

XMIN

2. Press 0 to define XMIN.

3. You can enter expressions to define values in the

window editor. Press

8.52.

4. Press. The expression is evaluated, and 4.25 isstored in XMAX. Press to accept XSCL as 1.

5. Press 04010 to define the YWindow variables.

Changing the Viewing Window

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12 Getting Started

Now that you have defined the function to be graphed and the window in whichto graph it, you can display and explore the graph. You can trace along afunction with TRACE.

1. Presss to graph the selected function in theviewing window.

The graph ofY1=(W2X)(L2X)X is shown in the

display.

2. Press~ once to display the free-moving cursor justto the right of the center of the screen. The bottom

line of the display shows the X- and Y-coordinate

values for the position of the graph cursor.

3. Use|,~,}, and to position the free-movingcursor at the apparent maximum of the function.

As you move the cursor, X- and Y-coordinate values

are updated continually to reflect the cursor position.

4. Pressr. The Trace cursor appears on the Y1function. 1 in the upper right corner of the display

shows that the cursor is on Y1. As you press| and~, you trace along Y1, one X dot at a time, evaluatingY1 at each X.

5. Press| and~ until you are on the maximum Yvalue. This is the maximum ofY1(X) for the X pixels.

(There may be a maximum value in between

pixels.)

Displaying and Tracing the Graph

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Getting Started 13

You can magnify the viewing window around a specific location using the Zoominstructions to help identify maximums, minimums, roots, and intersections offunctions.

1. Pressq to display the ZOOM menu.

This menu is typical of TI-80 menus. To select an

item, you may either press the number to the left of

the item, or you may press until the item number ishighlighted and then press.

2. To ZOOM IN, press 2. The graph is displayed again.

The cursor has changed to indicate that you are using

a Zoom instruction.

3. Use|,},~, and to position the cursor near themaximum value on the function, and press.

The new viewing window is displayed. It has been

adjusted in both the X and Y directions by factors of

4, the values for Zoom factors.

4. Pressp to display the new window variablevalues.

Zooming In on the Graph

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14 Getting Started

Getting Started has introduced you to basic calculator operation and the tableand function graphing features of the TI-80. The remainder of this Guidebookdescribes these features in more detail and also covers other capabilities of theTI-80.

You can enter fractions directly from the keyboard andperform calculations with fractions. You can convert between

fractions and their decimal equivalents. In MANSIMP mode,

you can simplify fractions step-by-step. The TI-80 tells you

when a fraction can be simplified and shows the common

factor after simplification (Chapter 3).

You can store, graph, and analyze up to four functions

(Chapter 4) and up to three parametric functions (Chapter 5).

You can use Draw operations to annotate graphs (Chapter 7).

You can create function evaluation tables to analyze multiple

functions simultaneously (Chapter 6).

You can enter and save up to six lists for use in statistical

analysis. You also can use lists to evaluate expressions at

multiple values simultaneously (Chapter 8).

You can perform one-variable and two-variable list-based

statistical analysis, including regression analysis, and plot the

data as histograms, points, x-y lines, or box-and-whisker plots.You can define and save three statistical plot definitions

(Chapter 9).

You can enter and save programs that include extensive

control and input/output instructions (Chapter 10)

Other TI.80 Features

Fractions

Graphing

Tables

Lists

Statistics

Programming

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Operating the TI-80 1-1

This chapter describes the TI.80 and provides general information about itsoperation.

Turning the TI.80 On and Off....................... 1-2

Setting the Display Contrast ........................ 1-3

The Display ...................................... 1-4

Entering Expressions and Instructions............... 1-6

The Edit Keys .................................... 1-8

Setting Modes .................................... 1-9

TI.80 Modes...................................... 1-10

Variable Names ................................... 1-12

Storing and Recalling Variable Values................ 1-13

Last Entry........................................ 1-14

Last Answer...................................... 1-16

TI.80 Menus

......................................

1-17The VARS and Y.VARS Menus...................... 1-19

EOS (Equation Operating System) .................. 1-20

Error Conditions.................................. 1-22

Chapter 1: Operating the TI-80

Chapter

Contents

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1-2 Operating the TI-80

To turn the TI.80 on, press the key. To turn it off, press and releasey, andthen press. After about five minutes without any activity, the APD(Automatic Power Down) feature turns the TI.80 off automatically.

Press to turn the TI-80 on.

If youpressedy to turn the calculator off, thedisplay shows the Home screen as it was when you last

used it, and errors are cleared.

If APD turned the calculator off, the display returns to thesame screen or editor in which you left it. See APD

(Automatic Power Down) below.

Press and release2, and then press to turn the TI-80

off. Any error condition is cleared.

All settings and memory contents are retained by theConstant Memory feature.

To prolong the life of the batteries, APD turns the TI-80 offautomatically after several minutes without any activity. When

you press, the calculator shows the same screen or editorin which you left it.

If an error message was displayed when APD turned theTI-80 off, the error is cleared, and the display returns to ablank line on the Home screen.

If a menu was displayed, the display returns to the screenor editor from which you called the menu.

All settings and memory contents are retained by the Constant

Memory feature.

Note: APD does not occur if a calculation or program is inprogress, unless the program is paused.

The TI-80 uses two CR2032 lithium batteries. To replace thebatteries without losing any information stored in memory,

follow the directions in Appendix B.

Turning the TI-80 On and Off

Turning the

Calculator On

Turning the

Calculator Off

APD

(Automatic

Power Down)

Batteries

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The brightness and contrast of the display depend on room lighting, batteryfreshness, viewing angle, and the adjustment of the display contrast. Thecontrast setting is retained in memory when the TI.80 is turned off.

You can adjust the display contrast to suit your viewing angle

and lighting conditions. As you adjust the contrast setting, the

display becomes lighter or darker. A highlighted number in the

upper right corner changes to indicate the current contrast

setting; 0 is the lightest, and 9 is the darkest.

To adjust the display contrast:

1. Press and release the2 key.

2. Use one of two keys:

To increase the contrast (darken the screen), press andhold7.

To decrease the contrast (lighten the screen), press andhold8.

Note: The display may become completely blank if you adjust

the contrast setting too low. If this happens, press and release

y, and then press and hold7 until the display reappears.

As you use the TI-80, the battery voltage will gradually drop,and the display will dim. You can adjust the contrast to darken

the display when this happens. If the display is dim and

adjusting the contrast to level 9 does not make it dark enough,

you should replace the batteries. Refer to Appendix B for

instructions on how to change the batteries.

Note: After you change batteries, the display contrast may

appear very dark. Press and releasey, and then press andhold8 to lighten the display.

Setting the Display Contrast

Adjusting the

Display Contrast

When to Replace

Batteries

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The TI.80 displays both text and graphs. Graphs are described in Chapters 4 and 5.

The primary screen of the TI-80 is the Home screen. You enterinstructions to be executed, expressions to be evaluated, and

see the results on the Home screen.When text is displayed, the TI-80 screen can show a maximumof eight lines with 16 characters each.

If all lines of the display are filled, text scrolls off the topof the display.

If an expression on the Home screen, the Y= editor(Chapter 4), or the program editor (Chapter 10) is longer

than one line, it wraps to the beginning of the next line.

On numeric editors such as the Window screen(Chapter 4), an expression scrolls to the left and right.

When an entry is executed on the Home screen, the answer is

displayed on the right side of the next line.

Entry Answer

The mode settings (pages 1-9 through 1-11) control the way

the calculator interprets expressions and displays answers.

If an answer is too long to display in its entirety, you can press

9 and6 to scroll the answer so that you can view all of it. Inthe second example below, the open brace without a

corresponding close brace indicates that the list is too long to

be displayed in its entirety.

Entry Answer

Answer Answer (scrolled)

To return to the Home screen from any other screen, press

y..

The Display

Home Screen

Displaying

Entries and

Answers

Returning to the

Home Screen

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In most cases, the appearance of the cursor indicates what

will happen when you press the next key.

Cursor Appearance Meaning

Entry Blinking 0 The next keystroke isentered at the cursor; it

types over any character.

INS (insert) Blinking_ The next keystroke isinserted at the cursor.

2nd Blinking The next keystroke is a2ndoperation.

ALPHA Blinking The next keystroke is an

alphabetic character.

memoryfull Checkerboard

rectangle

You have entered the

maximum number of

characters in a name, or

memory is full.

Graphs and the screens for viewing and editing tables and lists

have different cursors, which are described in the appropriate

chapters.

When the TI-80 is calculating or graphing, a vertical lineshows in the upper right of the display as a busy indicator.

During a pause in a program, the busy indicator is a dotted

line.

Display Cursors

Busy Indicator

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In most places where a value is required, you can use an expression to enter thevalue. You can enter instructions, which initiate an action, on the Home screenor in the program editor (Chapter 10).

An expression is a complete sequence of numbers, variables,

functions, and their arguments that evaluate to a single

answer. For example, pr is an expression. On the TI-80, youenter an expression in the same order as you would write it.

You can create expressions on the Home screen to calculate

an answer. In most places where a value is required, you can

use an expression to enter the value.

To create an expression, you enter numbers, variables, and

functions from the keyboard and menus. An expression is

completed when you press, regardless of the cursorlocation. The entire expression is evaluated according to

Equation Operating System (EOSTM) rules, and then the

answer is displayed.

Note: EOS rules determine the order in which operations are

completed (page 1-20).

Most TI-80 functions and operations are symbols with severalcharacters in them. You must enter the symbol from the

keyboard or menu. You cannot spell it out. For example, tocalculate the log of 45, you must pressl4 5. You cannottype in the letters L O G. (If you type LOG, the TI-80 interpretsthe entry as implied multiplication of the variables L, O, and G.)

Calculate 3.76 (-7.9 + 5) + 2 log45.

3.76ec7.9y]5d2l45

To enter more than one expression or instruction on a line,

separate them with a colon (:). They are all stored together in

Last Entry (page 1-15).

Entering Expressions and Instructions

Expressions

Entering an

Expression

Multiple Entries

on a Line

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To enter a number in scientific notation:

1. Type the part of the number that precedes the exponent.

This value can be an expression.

2. Press2^. is displayed.3. If the exponent is negative, press, and then type the

exponent, which can be one or two digits.

Entering a number in scientific notation does not cause the

answers to be displayed in scientific notation. The display

format is determined by the mode settings (pages 1-9 through1-11) and the size of the number.

A function returns a value. For example, , , , +, , and LOGare functions. Some functions take more than one argument,

which is indicated by a( at the end of the name. MIN(requires

two arguments in this example: MIN(5,8).

An instruction initiates an action. For example, CLRDRAWis

an instruction that clears any drawn elements from a graph.

Instructions cannot be used in expressions. Some instructions

take more than one argument, which is indicated by a( at theend of the name. LINE( requires four arguments in this

example: LINE(1,1,3,3).

While the busy indicator is displayed, indicating that a

calculation or a graph is in progress, you can press to stopthe calculation. (There may be a delay.)

Entering a

Number in

Scientific

Notation

Functions

Instructions

Interrupting a

Calculation

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The arrow keys near the upper right of the keyboard control the movement ofthe cursor. In normal entry, a keystroke types over the character or charactersat the position of the cursor. The4 andy/ keys delete or insertcharacters.

Key(s) Action(s)

9 or6 Moves the cursor within an expression. These keys repeatwhen you hold them down.

7 or8 Moves the cursor between lines within an expression. Thesekeys repeat when you hold them down.

On the top line of an expression on the Home screen,7moves the cursor to the beginning of the expression.

On the bottom line of an expression on the Home screen,

8moves the cursor to the end of the expression.

26 Moves the cursor to the beginning of an expression.

29 Moves the cursor to the end of an expression.

Evaluates an expression or executes an instruction.

M On a line with text on the Home screen, clears (blanks) thecurrent line.

On a blank line on the Home screen, clears everything on

the Home screen.

In an editor, clears (blanks) the expression or value wherethe cursor is located; it does not store a zero.

4 Deletes the character at the cursor. This key repeats.

y/ Lets you insert characters at the underline cursor. To endinsertion, pressy/ or a cursor key.

y Next key press is a2nd operation (the gold-colored labelprinted to the left above a key). The cursor changes to. Tocancel 2nd, pressy again.

? Next key press is an ALPHA character (the light graycharacter to the right above a key). The cursor changes to A.

To cancel ALPHA, press? or a cursor key.

y< Sets ALPHA-LOCK; each subsequent key press results in anALPHA character. The cursor changes to . To cancel

ALPHA-LOCK, press?.

@ Allows you to enter an X in FUNC mode or aT in PARAM

mode without pressing? first.

The Edit Keys

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Modes control how numbers and graphs are displayed and interpreted by thecalculator. Mode settings are retained by the Constant Memory feature when theTI.80 is turned off.

Press3to display the MODE screen. The current settingsare highlighted. The settings are described on the following

pages.

NORMAL SCI Numeric display format.

FLOAT 0123456789 Number of decimal places.

RADIAN DEGREE Unit of angle measure.

abc bc Type of fraction display.AUTOSIMP MANSIMP Whether to simplify fractions.

FUNC PARAM Type of graphing.

CONNECTED DOT Whether to connect graph points.SEQUENTIAL SIMUL Whether to plot simultaneously.

To change the mode setting:

1. Press8 or7 to move the cursor to the line of the settingthat you want to change. The setting that the cursor is on

blinks.

2. Press9 or6 to move the cursor to the setting that you

want.

3. Press.

To leave the MODE screen:

Press the appropriate keys to go to another screen.

Pressy. orM to return to the Home screen.

You can set a mode from a program by entering the name of

the mode as an instruction; for example, FUNC orFLOAT.

From a blank line in the program editor (Chapter 10), press

3to display a menu of the mode names, and then selectthe name. The name is copied to the cursor location.

Setting Modes

Checking MODE

Settings

Changing MODE

Settings

Leaving the

MODE Screen

Setting a Mode

from a Program

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The TI.80 has eight mode settings. They control how numeric entries areinterpreted, how answers are calculated or displayed, and how graphs appear inthe display. Modes are set on the MODE screen (page 1.9).

Notation formats affect only how an answer is displayed on

the Home screen. Numeric answers can be displayed with up

to 10 digits and a two-digit exponent. You can enter a number

in any format.

NORMAL display format is the way in which we usually

express decimal numbers, with digits to the left and right of

the decimal, as in 12345.67.

SCI (scientific) notation expresses numbers in two parts. The

significant digits can be displayed with one digit to the left of

the decimal. The appropriate power of 10 displays to the rightof, as in 1.2345674.Note: If you select normal display format, but the answer

cannot be displayed in 10 digits or the absolute value is less

than .001, the TI-80 displays the answer in scientific notation.

Decimal settings affect only how an answer is displayed on

the Home screen. You can enter a number in any format. The

decimal settings apply to both notation formats.

FLOAT (floating) decimal setting displays up to 10 digits, plusthe sign and decimal.

The fixed decimal setting lets you select the number of digits

(0 to 9) to be displayed to the right of the decimal. The

displayed value is rounded based on the number of digits you

selected. The actual value is stored and used in calculations.

Place the cursor on the number of decimal digits you want,

and press.

Note: In the program editor, the format for fixed decimalsettings is FIXn. Entern as an integer from 0 to 9. The mode

is changed to fixed decimal when the program is executed.

TI-80 Modes

NORMAL

SCI

FLOAT

Fixed Decimal

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The angle mode controls:

How the calculator interprets angle arguments in SIN,COS, TAN, and polar-to-rectangular conversions.

How the calculator returns angle answers to SIN, COS,TAN, and rectangular-to-polar conversions.

RADIAN mode interprets angle arguments as radians and

returns angle answers in radians.

DEGREE mode interprets angle arguments as degrees and

returns angle answers in degrees.

abcdisplays fraction results as mixed numbers; forexample, the result of13 + 43 is displayed as 123.bc displays fraction results as simple fractions; for example,the result of13 + 43 is displayed as 53.AUTOSIMPautomaticallysimplifies fraction results to their

lowest terms before displaying them; for example, the result

of26 + 26 is displayed as 23.MANSIMP displays fraction results without automatic

simplification; for example, the result of26 + 26 isdisplayed as 46.FUNC (function) graphing plots functions where Y isexpressed in terms ofX (Chapter 4).

PARAM (parametric) graphing plots relations where X and Y

are each expressed in terms ofT (Chapter 5).

CONNECTED draws line segments between the calculated

points of the selected functions.

DOT plots only the calculated points of the selected functions.

SEQUENTIAL graphing evaluates and plots one functioncompletely before the next function is evaluated and plotted.

SIMUL (simultaneous) graphing evaluates and plots all

selected functions for a single value ofX,one at a time. In

Parametric mode, X and Y are selected pairs. They are

evaluated and plotted aT value at a time.

RADIAN

DEGREE

abcbc

AUTOSIMP

MANSIMP

FUNCPARAM

CONNECTED

DOT

SEQUENTIALSIMUL

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On the TI.80 you can enter, name, and use several types of data: numeric values(including fractions), lists, functions, and statistical plots.

The TI-80 uses both user-assigned and pre-assigned names forvariables and other items saved in memory.

Variable Type Names

Numeric values

(including fractions)

A, B, ..., Z, q (single character only).

Lists L1, L2, L3, L4, L5, L6 (on the

keyboard).

Functions Y1, Y2, Y3, Y4 (on the Y= editor in

FUNC mode).Parametric equations X1/Y1X2/Y2, X3/Y3 (on the Y=

editor in PARAM mode).

Statistical plots PLOT1, PLOT2, PLOT3(on the

STAT PLOTS menu).

System variables XMIN, XMAX, and others (on various

menus).

Programs have user-defined names also and share memorywith variables. Program names can be up to seven characters

long. Programs are entered and edited from the program

editor (Chapter 10).

You can store to lists (Chapter 8), system variables such as

XMAX(Chapter 4) orTBLMIN(Chapter 6), and all Y=functions (Chapters 4 and 5) from the Home screen or from a

program. You can store to lists (Chapters 8 and 9) and

functions (Chapters 4 and 5) from editors. You can also store

to a list element (Chapter 8).

For more information about system variables, see Appendix A.

Variable Names

Variables and

Defined Items

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Values are stored to and recalled from memory using variable names. When anexpression containing the name of a variable is evaluated, the value of thevariable at that time is used.

You can store a value to a variable from the Home screen or a

program using the key. Begin on a blank line.

1. Enter the value that you want to store (this can be an

expression).

2. Press. The symbol ! is copied to the cursor location.

3. Press? and then the single letter of the variable towhich you want to store the value.

4. Press. If you entered an expression, it is evaluated.

The value is stored in the variable.

To display the value of a variable, enter the variable name on a

blank line on the Home screen, and then press. You canenter the name of the variable in one of the following ways:

Press? and the letter of the variable (for user-definedvariables).

Press2 and the name of the list.

PressL and select the type and name of the variable(for system variables).

Press2G and select the type and name of thefunction.

To use the current value of a variable in an expression, just

enter the variable name in the expression.

Storing and Recalling Variable Values

Storing Values in

a Variable

Displaying a

Variable Value

Using a Variable

in an Expression

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When you press on the Home screen to evaluate an expression or executean instruction, the expression or instruction is stored in an area called LastEntry, which you can recall. When you turn the TI.80 off, Last Entry is retained inmemory.

You can recall Last Entry and edit it from the Home screen.Pressy. The current line is cleared, and the LastEntry is copied to the line. The cursor is positioned at the end

of the entry. Because the TI-80 updates the Last Entry storagearea only when you press, you can recall the previousentry even if you have begun entering the next expression.

However, when you recall Last Entry, it replaces what you

have typed.

57y

The TI-80 keeps previous entries (up to a total of 80 bytes) inLast Entry. You can display and edit those entries by

continuing to press2. Last Entry displays previousentries in a loop, beginning with newest entry and moving to

the oldest entry. Once the oldest item is displayed,2displays the newest item again.

1?A2?B3?Cy

When you pressyagain, the previous item replaces

the item on the current line.

2

Last Entry

Using Last Entry

Displaying a

Previous Entry

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To execute Last Entry, press on a blank line on theHome screen. The entry is executed, but it does not display

again.

0?N?N1?N

To enter more than one expression or instruction on a line,

separate them with a colon (:). They are all stored together in

Last Entry.

If the previous entry contained more than one expression or

instruction, separated with a colon (page 1-6), they all arerecalled. You can recall all entries on a line, edit any of them,

and then execute all of them.

Using the equation A=pr2, use trial and error to find the radiusof a circle that covers 200 square centimeters. Use 8 as your

first guess.

8?RyyT?Ray

Now try this.

y67y/.95

Continue until the answer is as accurate as you want.

Re.executing thePrevious Entry

Multiple Entries

on a Line

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When an expression is evaluated successfully from the Home screen or from aprogram, the TI.80 stores the answer to a variable, ANS (Last Answer). ANS maybe a decimal number, a fraction, or a list. When you turn the TI.80 off, the valuein ANS is retained in memory.

You can use the variable ANS to represent the last answer inmost places. When you pressy, the variable name ANSis copied to the cursor location. When the expression is

evaluated, the TI-80 uses the value ofANS in the calculation.

Calculate the area of a garden plot that is 1.7 meters by 4.2

meters. Then calculate the yield per square meter if the plot

produces a total of 147 tomatoes.

1.7p4.2

147ey

You can use the value in ANS as the first entry in the next

expression without entering the value again or pressingy

. On a blank line on the Home screen, enter the function.The TI-80 types the variable name ANSfollowed by thefunction.

5e2p9.9

To store an answer, store ANSto a variable before you

evaluate another expression.

Calculate the area of a circle of radius 5 meters. Thencalculate the volume of a cylinder of radius 5 meters and

height 3.3 meters. Store the result in the variable V.

yT5ap3.3?V

Last Answer

Using LastAnswer (ANS) in

an Expression

Continuing an

Expression

Storing Answers

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To leave the keyboard uncluttered, the TI.80 uses full.screen menus to give youaccess to many additional operations. The use of specific menus is described inthe appropriate chapters.

Some menu keys, such asI, display more than one menu.The names of the menus appear on the top line. The current

menu is highlighted and the items in that menu are displayed.

Press9 or6 to move the cursor to a different menu.

The number of the current item is highlighted. If there are

more than seven items on the menu, a$ appears on the lastline in place of the : (colon) between the menu number and

name. Menu items, such as VARS WINDOW, that end in ...

(ellipsis marks) display another menu.

There are two methods of selecting from a menu.

Press the number of the item you want to select.

Press8 and7 to move the cursor to the item you want toselect, and then press.

Calculate 27 .

1. PressI to display the MATH menu.

2. To select , you may either press 4 or press888.

3. Enter 27, and then press to evaluate the expression.

TI-80 Menus

Moving from One

Menu to Another

Selecting an Item

from a Menu

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There are several ways to leave a menu without making a

selection from the menu.

To return to the Home screen, press2..

To return to the screen where you were, pressM. To display a different menu, press the appropriate key,

such as*.

To select another screen, press the appropriate key, suchas).

Leaving a Menu

without Making a

Selection

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You may want to use the names of system variables (such as XMIN) andfunctions (such as Y1) in an expression. You may also want to store valuesdirectly to those variables. Use the VARS or Y.VARS menus to access thenames.

The VARS menu displays the names of window variables suchas XMIN and TSTEP, statistics variables such as v andQ1, andtable variables such as TBLMIN.

PressL to display the VARS menu. Some of the itemsdisplay more than one menu of variable names.

VARS

1: WINDOW... Names ofX, Y, and T variables.2: STATISTICS... X/Y, G, EQ, and BOX variables.

3: TABLE...

TBLMIN and @TBL variables.4: SIMPFACTOR... Factor last used by SIMP function.

The Y.VARS menus display the names of functions and theinstructions to select or deselect functions from a program or

the Home screen.

Press2G to display the Y.VARS menu. Then press9or6 to select the type of variable you want.

Y Displays a menu of names of Yn

functions.XTYT Displays a menu of names of XnTYnT equations.ONOFF Lets you select/deselect functions.

To copy a variable name from aVARS orY.VARS menu:

1. PressL or2G. The VARS orY.VARS menu isdisplayed.

2. Select the type of variable you want.

3. Press to select the name you want from the menu. Itis copied to the cursor location.

The VARS and Y.VARS Menus

VARS Menu

Y.VARS Menu

Copying a Name

from a VARS or

Y.VARS Menu

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The Equation Operating System (EOS) defines the order of operations for thecalculatorthat is, the order in which the TI.80 evaluatesfunctions inexpressions. EOS lets you enter numbers and functions in a simple,straightforward sequence.

A function returns a value. EOS evaluates the functions in anexpression in the following order.

1 Functions that are entered after the argument, such as

A, 2, 22!, 45, 2p, and SIMP.2 Powers and roots, such as 2^5 or532.3 Implied multiplication where the second argument is a

number, variable name, or list, or begins with an open

parenthesis, such as 4A, (A+B)4,or4(A+B).

4 Single-argument functions that precede the argument,

such as LA, 63, SIN B, orLOG 3.

5 Implied multiplication where the second argument is a

multi-argument function or a single-argument function

that precedes the argument, such as 2NDERIV(A,A,6) orASIN 2.

6 Permutations (nPr) and combinations (nCr).

7 Multiplication and division (including INT).

8 Addition and subtraction.

9 Test functions, such as>or.

10 Conversion functions: 8FRAC, 8DEC, 8abc, and 8bc.Within a priority group,EOS evaluates functions from left toright. However, two or more single-argument functions that

precede the same argument are evaluated from right to left.For example, SIN FPART LN 8 is evaluated as

SIN(FPART(LN 8)).

Calculations within a pair of parentheses are evaluated first.

Multi-argument functions, such as NDERIV(A,A,6), areevaluated as they are encountered.

The conversion functions 8FRAC, 8DEC, 8abc, and 8bccan be used only at the end of a command line with one

exception: they can be followed by a store instruction.

EOS (Equation Operating System)

Order ofEvaluation

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The TI-80 recognizes implied multiplication. For example, itunderstands 2p, 4SIN 45, 5(1+2), and (25)7 as impliedmultiplication.

All calculations inside a pair of parentheses are completed

first. For example, in the expression 4(1+2), EOS firstevaluates the portion inside the parentheses, 1+2, and then

multiplies the answer, 3, by 4.

You can omit any right (closing) parenthesis at the end of an

expression. All open parenthetical elements are closed

automatically at the end of an expression and preceding the !(store) or display-conversion instructions.

Note: Parentheses are also used to enclose the arguments for

certain functions, for example, NDERIV(A,A,6). In thesecases, parentheses do not indicate implied multiplication.

To enter a negative number, use the negation function. Press

, and then enter the number. On the TI-80, negation is in thefourth group in the EOS hierarchy. Functions in the first

group, such as squaring, are evaluated before negation.

For example, LX is a negative number (or 0); L9 is L81. Useparentheses to square a negative number: (L9).

Note: Use the| key for subtraction and the key fornegation. If you press| to enter a negative number, as in 9p|7, or if you press to indicate subtraction, as in 9 7, itis an error. If you press?A?B, it is interpreted

as implied multiplication (A QLB).

Implied

Multiplication

Parentheses

Negation

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The TI.80 detects any errors at the time it evaluates an expression, executes aninstruction, plots a graph, or stores a value. Calculations stop and an errormessage with a menu is displayed immediately. Error codes and conditions aredescribed in detail in Appendix B.

If the TI-80 detects an error, it displays the error screen.

The top line indicates the general type of error, such as

SYNTAX orDOMAIN. For additional information about each

error message, see Appendix B.

If you select GOTO, the cursor is displayed at the locationwhere the error was detected.

Note: If a syntax error was detected in the contents of a

Y= function during program execution, GOTO returns the

user to the Y= editor, not to the program.

If you select QUIT, or pressy. orM, you returnto the Home screen.

To correct an error:

1. Note the type of the error.

2. Select GOTO, if that option is available; and look at the

expression for syntax errors, especially at and before the

cursor location.

3. If the error in the expression is not readily apparent, turn

to Appendix B, and read the information about the error

message.

4. Correct the expression.

Error Conditions

Diagnosing anError

Correcting an

Error

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Math, Angle, and Test Operations 2-1

This chapter describes the math, angle, and relational operations that areavailable on the TI.80. The most commonly used functions are accessed fromthe keyboard; others are accessed through menus.

Getting Started: Lottery Chances .................... 2-2

Using the TI-80 Functions.......................... 2-3

Keyboard Math Operations ......................... 2-4

MATH MATH Operations ........................... 2-7

MATH NUM (Number) Operations ................... 2-10

MATH PRB (Probability) Operations................. 2-12

ANGLE Operations................................ 2-14

TEST (Relational) Operations....................... 2-16

Chapter 2: Math, Angle, and Test Operations

Chapter

Contents

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2-2 Math, Angle, and Test Operations

Getting Started is a fast-paced introduction. Read the chapter for details.

Suppose you want to enter a lottery where six numbers will be drawn out of 50.To win, you must pick all six numbers (in any order). What is the probability ofwinning if you buy one ticket? What is the probability of winning if you buy fivetickets?

1. Determine the number of combinations possible. On

the Home screen, press 50 to enter the total number of

items. PressI6 to display the MATH PRB menu.Press 3 to select nCr. Press 6 to enter the number of

items selected.

2. Press to evaluate the expression. This is thetotal number of possible combinations of 6 numbers

drawn from a set of 50 numbers. With one ticket, you

have one chance in 15,890,700 of winning.

3. To calculate the probability of winning with one

ticket, press 1e2. The answer is toolarge to display in fixed notation; therefore, it is shown

in scientific notation. 0.00000006292988981 is thedecimal equivalent.

4. To calculate the probability of winning with five

tickets, pressp5. Again, the answer is toosmall to display in fixed notation. The decimal

equivalent is 0.000000314649449.

Getting Started: Lottery Chances

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This page contains some general information you should know about the TI.80functions described in Chapter 1.

Functions that are valid for lists return a list calculated on an

element-by-element basis. If two lists are used in the same

expression, they must be the same length. For more

information about lists, see Chapter 8.

Some math functions (+,, , ,x, bc, abc, DEC)accept fractions as input values.All other functions convert

fractions to decimals before operating on them. For more

information about fractions, see Chapter 3.

Using the TI-80 Functions

Using Lists with

Functions

Using Fractions

with Functions

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The most commonly used math functions are on the keyboard. The keyboardmath operations can be used with decimal numbers, fractions (except as noted),expressions, and lists.

The basic arithmetic functions are: addition, subtraction|,multiplicationp, and divisione. Each argument for thesefunctions can be a list.

valueA+valueB, valueAvalueB,valueAvalueB, valueAvalueB

The trigonometric functions are interpreted according to thecurrent RADIAN/DEGREE mode setting. (Refer to page 1-9 for

instructions on changing the mode setting.) For example,

SIN 30 in RADIAN mode returns L.9880316241; in DEGREE

mode, it returns .5. Each argument for the trigonometric

functions may be a list.

SINvalue, COSvalue, TANvalue

SIN, COS, and TAN are the inverse trig functions (arcsine,arccosine, and arctangent).

SINvalue, COSvalue, TAN valueRADIAN Mode

(inverse,V) may be used with numbers, expressions, orlists. The multiplicative inverse is the equivalent of thereciprocal, 1x.

value

Keyboard Math Operations

+ (Add)

(Subtract)

(Multiply) (Divide)

Trig Functions

(Inverse)

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^ (power,Z), 2 (square,a), and (square root,2]) maybe used with decimal numbers, fractions, expressions, or lists.

When used with a fraction, returns a decimal number.

value power, value2, value

Note: Raising a negative number to a noninteger power can

result in a complex number, which returns an error.

These functions find the logarithml, power of ten2h,

and natural logx of the specified value or list of values.

LOGvalue, 10 power, LNvalue

e^ (2s) returns the constant e raised to a power or list of

powers. e^1 returns the value of the constant e.

e power

^ (Power)2(Square)(Square Root)

LOG

10^LN

e^

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L(negation,) returns the negative of a number, expression,or list. The narrow negation symbol (L) distinguishes negation

from the subtraction or minus ().

Lvalue

EOS rules (Chapter 1) determine when negation is evaluated.

For example, LA2 returns a negative number because squaring

is evaluated before negation. Use parentheses to square a

negated number, (LA)2.

ABS (absolute value,2P) returns the absolute value of a

number, expression, or list.

ABSvalue

Pi (2T) is stored as a constant in the TI-80. Press2Tto copy the symbol p to the cursor location. The number

3.141592654 is displayed forp, but 3.1415926535898 is usedinternally in calculations.

L(Negation)

ABS

p (Pi)

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To display the MATH MATH menu, pressI. When you select a menu item, thename is copied to the cursor location. Functions that are valid for lists return alist calculated on an element-by-element basis.

MATH NUM PRB

1: INT Displays quotient and remainder.

2: 8DEC Displays answer in decimal form.

3: 3 Cube.4: 3 Cube root.5: x nth root.6: NDERIV( Numerical derivative.

On the Home screen or from a program, INT(integer divide,

MATH MATH, item 1) returns the quotient (or quotient and

remainder) resulting from the division of two integers. Eachargument can be a list.

integerAINTintegerB

When INT is executed on the Home screen, it displays the

symbols Q= for the quotient and R= for the remainder.

Note: IfINT is embedded in an expression, Q= and R= may

not be displayed.

When used with lists, INTreturns a list of quotients only.If the result ofINT is used in subsequent calculations, the

remainder is dropped, and only the quotient is used.

The quotient from INT is returned to ANS.

MATH MATH Operations

MATH MATH

Menu

INT

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8DEC (convert to decimal, MATH MATH, item 2) displays an

answer in decimal form. 8DEC can only be used after avalue

and at the end of an expression. value can be a list.

value8DEC

expression8DEC

3 (cube, MATH MATH, item 3) returns the cube of a number,

expression, or list.

value3

3 (cube root, MATH MATH, item 4) returns the cube root of a

number, expression, or list.

3value

x(root, MATH MATH, item 5) returns thenth real root of anumber, expression, or list.

nthrootxvalue

8DEC

3 (Cube)

3(Cube Root)

x(Root)

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NDERIV( (numerical derivative, MATH MATH, item 6) returns

an approximate derivative of an expression with respect to a

specified variable, given the value at which to calculate the

derivative, and H (optional; if none is specified, 1-3 is used).NDERIV(expression,variable,value) orNDERIV(expression,variable,value,H)

NDERIV( uses the symmetric difference quotient method (as

shown in the formula below), which approximates the

numerical derivative value as the slope of the secant line

through the points:

f(X+H)f(XH)f(x) =

2H

As H gets smaller, the approximation usually gets more

accurate.

Because of the method used, NDERIV( can return a false

derivative value at a nondifferentiable point.

NDERIV(

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To display the MATH NUM menu, pressI9. When you select a menu item,the name is copied to the cursor location. Functions that are valid for lists returna list calculated on an element-by-element basis.

MATH NUM PRB

1: ROUND( Round.2: IPART Integer part.3: FPART Fractional part.4: INT Greatest integer.5: MIN( Minimum value.6: MAX( Maximum value.7: REMAINDER( Remainder of a division result.

ROUND( (MATH NUM, item 1) returns a number, expression,

or list rounded to a specified number of decimals (9). If thenumber of decimals is omitted, the number is rounded to the

digits that are displayed, a maximum of 10 digits.

Round(value,#decimals) Round(value)

ZPART (integer part, MATH NUM, item 2) returns the integer

part or parts of a number, expression, or list. FPART

(fractional part, MATH NUM, item 3) returns the fractional

part or parts of a number, expression, or list.

ZPARTvalue FPARTvalue

INT (greatest integer, MATH NUM, item 4) returns the largest

integer less than or equal to a number, expression, or list. The

value is the same asZPARTfor nonnegative numbers andnegative integers, but one integer less than ZPARTfor negative

noninteger numbers.

INT value

MATH NUM (Number) Operations

MATH NUM

Menu

ROUND(

ZPART

FPART

INT

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MIN( (minimum value, MATH NUM, item 5) returns the smaller

of two values or the smallest element in a list. If two lists are

compared, it returns a list of the smaller of each pair of

elements. If a list and a value are compared, it compares each

element in the list to the value.MAX( (maximum value, MATH NUM, item 6) returns the larger

of two values or the largest element in a list. If two lists are

compared, it returns a list of the larger of each pair of

elements. If a list and a value are compared, it compares each

element in the list to the value.

MIN(valueA,valueB) MAX(valueA,valueB)

MIN(list) MAX(list)

MIN(listA,listB) MAX(listA,listB)

MIN(value,list) MAX(value,list)

MIN(list,value) MAX(list,value)

Note:MIN( and MAX( are also available on the LIST MATH

menu.REMAINDER( (MATH NUM, item 7) returns the remainder

resulting from the division of two integers, each of which can

be a list. (See INT, page 27.)

REMAINDER(valueA,valueB) REMAINDER(listA,listB)

REMAINDER(value,list) REMAINDER(list,value)

If a list is used as one or both arguments, the result is a list of

remainders.

MIN(

MAX(

REMAINDER(

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To display the MATH PRB menu, pressI6. When you select a menu item,the name is copied to the cursor location. Functions that are valid for lists returna list calculated on an element-by-element basis.

MATH NUM PRB

1: RAND Random number generator.2: nPr Number of permutations.3: nCr Number of combinations.4: ! Factorial.5: RANDINT( Random integer generator.

RAND (random number, MATH PRB, item 1) generates and

returns a random number greater than 0 and less than 1 (as in

the first example below). A random number is generated from

a seed value. To control a random number sequence, firststore an integer seed value in RAND. In the second example

below, 1 is stored to RAND so that the TI-80 uses 1 as the seed

value for generating random numbers.

Note: When you reset the TI-80, RAND is set to the factory

seed value, which is 0.

MATH PRB (Probability) Operations

MATH PRB

Menu

RAND

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nPr (number of permutations, MATH PRB, item 2) returns the

number ofpermutations ofitems takennumberat a time.

items andnumbermust be nonnegative integers. Both items

andnumbercan be lists.

nCr (number of combinations, MATH PRB, item 3) returns thenumber ofcombinations ofitems takennumberat a time.

items andnumbermust be nonnegative integers. Both items

andnumbercan be lists.

itemsnPrnumber

itemsnCrnumber

!(factorial, MATH PRB, item 4) returns the factorial of a

positive integer or list of integers between 0 and 69.

value!

RANDINT( (random integer, MATH PRB, item 5) generates a

random integer within a specified range. It requires two

arguments: the lower and upper boundaries of the range (in

any order). Both arguments must be integers. Both arguments

can be negative. Both arguments can be lists.

RANDINT(lower,upper)

nPr

nCr

! (Factorial)

RANDINT(

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To display the ANGLE menu, press2E. The ANGLE menu displays angleindicators and instructions. When you select an item from the menu, the name iscopied to the cursor location.

ANGLE

1: Degree notation.

2: r Radian notation.3: R8Pr( Returns r, given X and Y.4: R8Pq( Returns q, given X and Y.5: P8Rx( Returns x, given R and q.6: P8Ry( Returns y, given R and q.

(degree, ANGLE, item 1) lets you designate an angle or list of

angles as degrees, regardless of the current angle mode

setting. In RADIAN mode, can also be used to convertdegrees to radians.

value

RADIAN Mode

r (radians, ANGLE, item 2) lets you designate an angle or list

of angles as radians, regardless of the current angle modesetting. In DEGREE mode, r can also be used to convert

radians to degrees.

valuer

DEGREE Mode

ANGLE Operations

ANGLE

Menu

(Degree)

r (Radians)

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Note: When converting from one coordinate system to the

other, be sure that the angle mode setting, DEGREE or

RADIAN, is appropriate for your angle measurements. (Press

3to check the current setting.)

R8Pr( (ANGLE, item 3) converts the given rectangularcoordinates to polar coordinates and returns r.

R8Pq((ANGLE, item 4) converts the given rectangular

coordinates to polar coordinates and returns q.

BothXand Ycan be lists.

R8Pr(X,Y)

R8Pq(X,Y)

RADIAN Mode

P8Rx((ANGLE, item 5) converts the given polar coordinates

to rectangular coordinates and returns x.

P8Ry( (ANGLE, item 6) converts the given polar coordinates

to rectangular coordinates and returns y.

BothR and q can be lists.

P8Rx(R,q)

P8Ry(R,q)

RADIAN Mode

R8Pr (

R8Pq(

P8Rx(

P8Ry(

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To display the TEST menu, press2D. When you select from the menu, thename is copied to the cursor location. These functions are valid for lists; theyreturn a list calculated on an element-by-element basis.

TEST True if:1:= Equal.2: Not equal to.3:> Greater than.4: Greater than or equal to.5:< Less than.6: Less than or equal to.

Relational operators compare valueA and valueB and return 1

if the test is true or0 if the test is false. valueA and valueB can

be numbers, expressions, or lists.

Relational operators are often used in programs to control

program flow and in graphing to control the graph of a

function over specific values.

valueA=valueB

valueAvalueB

valueA>valueB

valueAvalueB

valueA Shades an area.

7: SHADE_Y< Shades an area.

8: SHADE( Shades an area.

9: GRIDON Turns the graph grid on.

0: GRIDOFF Turns the graph grid off.

(See page 7-12 for an explanation ofCLRDRAW.)

Because Draw operations draw on top of the graph of

currently selected functions, you may want to do one or more

of the following before drawing on a graph:

Change the mode settings.

Enter or edit functions in the Y= list.

Select or deselect functions in the Y= list.

Change Window variable values.

Turn STAT PLOTS on or off.

Clear existing drawings with CLRDRAW (page 7-12).

Draw operations can draw on FUNC and PARAM graphs. The

coordinates for all Draw instructions are always the

X-coordinate and Y-coordinate values of the display.

You can use most of the operations from the DRAW DRAW

and DRAW POINTS menus to draw directly on a graph, using

the cursor to identify coordinates; or you can execute these

instructions from the Home screen or a program.

DRAW DRAW Menu

DRAW DRAW

Menu

Before Drawing

on a Graph

Drawing on a

Graph

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7-4 Draw Operations

While a graph is displayed, LINE( lets you use the cursor to define a line on thegraph. If a graph is not displayed, the instruction is copied to the Home screen.

To define a line directly on a graph:

1. When a graph is displayed, select LINE( from theDRAW DRAW menu (item 2).

2. Position the cursor at the beginning point of the line you

want to draw. Press.

3. Move the cursor to the end point of the line you want to

draw. The line is displayed as you move the cursor. Press

.

To continue to draw lines, repeat steps 2 and 3. To cancel

LINE(, pressM.

LINE( (DRAW DRAW, item 2) draws a line between the

coordinates (X1,Y1) and (X2,Y2). The values may be enteredas expressions.

LINE(X1,Y1,X2,Y2)

For example, enterLINE(0,0,6,9) on the Home screen, and

then press.

Drawing Lines

Directly on a

Graph

From the Home

Screen or aProgram

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Draw Operations 7-5

While a graph is displayed, HORIZONTAL and VERTICAL let you define lines onthe graph using the cursor. If a graph is not displayed, the instruction is copiedto the Home screen.

To draw horizontal and vertical lines directly on a graph:

1. When a graph is displayed, select HORIZONTAL (item 3)

orVERTICAL (item 4) from the DRAW DRAW menu.

2. A line is displayed that moves as you move the cursor.

Position the cursor where you want to draw the line. Press

. The line is drawn on the graph.

To continue to draw lines, repeat step 2. To cancel

HORIZONTAL orVERTICAL, pressM.

HORIZONTAL (DRAW DRAW, item 3) draws a horizontal line

at Y=Y(which can be an expression, but not a list).

HORIZONTAL Y

VERTICAL (DRAW DRAW, item 4) draws a vertical line at

X=X(which can be an expression, but not a list).

VERTICALX

Note: In the example above, the horizontal line is drawn first,

and then the vertical line is drawn.

Drawing Horizontal and Vertical Lines

Directly on a

Graph

From the Home

Screen or a

Program

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7-6 Draw Operations

DRAWF (draw function) draws a function on the current graph. DRAWF must beentered on the Home screen or in the program editor.

DRAWF (draw function, DRAW DRAW, item 5) is not an

interactive operation. It draws the specified expression as a

function in terms ofX on the current graph.

DRAWFexpression

For example, ifY1=.2X2X+6 is the only selected function,DRAWF Y15 plots Y1and then draws the function Y15

when you press.

Note: You cannot trace on DRAWF functions.

GRIDON (DRAW DRAW, item 9) and GRIDOFF

(DRAW DRAW, item 0) set graphs to be drawn with the grid

points on or off, respectively. The grid points correspond to

the axes tick marks. The default for the TI-80 is GRIDOFF.1. From the Home screen, press2F to display the

DRAW menu.

2. Press 9 to select GRIDON, or press 0 to select GRIDOFF.

3. Press. The message DONE is displayed. The nexttime the graph is displayed, the grid points will be on if

you selected GRIDON, or off if you selected GRIDOFF.

Drawing a Function

Drawing a

Function

Using GRIDON

and GRIDOFF

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Draw Operations 7-7

There are three shading instructions on the DRAW DRAW menu: SHADE_Y>,SHADE_Y (DRAW DRAW, item 6) takes up to four

arguments (functions ofX).

SHADE_Y>function

SHADE_Y>function1, . . . ,function4

When executed, SHADE_Y> plots the specified function(s) on

the graph and shades the area above the function with a

pattern.

The patterns for shading are automatically assigned in the

following order.

Function 1 Vertical pattern.

Function 2 Diagonal pattern, lower left to upper right.

Function 3 Diagonal pattern, upper left to lower right.

Function 4 Horizontal pattern.

When you specify multiple functions, the shading is done

sequentially.

Shading Areas on a Graph

Shading Areas

above a Function

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7-8 Draw Operations

SHADE_Y< (DRAW DRAW, item 7) takes up to four

arguments (functions ofX).

SHADE_Y

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Draw Operations 7-9

SHADE( (DRAW DRAW, item 8) shades the area on a graph

that is below one specified function and above another,

between two X values. SHADE( is not an interactive operation.

It draws lowerfunc and upperfunc in terms of X on the

current graph and shades the area that is specifically abovelowerfunc and below upperfunc. Only the areas where

lowerfunc < upperfunc are shaded.

You can specify the shading resolution (an integer between 1

and 9). If none is specified, 1 is used.resolution=1 shades

every pixel.resolution=2 shades every second pixel.

resolution=3 shades every third pixel, and so on.

Optionally, you can specifyXleft (the left boundary) and

Xright (the right boundary) for the shaded area. IfXleft or

Xright is not specified, XMIN and XMAX are used.

SHADE(lowerfunc,upperfunc)

SHADE(lowerfunc,upperfunc,resolution)

SHADE(lowerfunc,upperfunc,resolution,Xleft)

SHADE(lowerfunc,upperfunc,resolution,Xleft,Xright)

Shading a Graph

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7-10 Draw Operations

To display the DRAW POINTS menu, press2F9. What happens whenyou select an item from this menu depends on whether or not a graph isdisplayed when you access the menu, as described under each operation.

DRAW POINTS

1: PT-ON( Turn on a point.

2: PT-OFF( Turn off a point.

3: PT-CHANGE( Toggle a point on or off.

To draw points directly on a graph:

1. When a graph is displayed, select PT.ON( from the

DRAW POINTS menu (item 1).

2. Position the cursor at the location on the display where

you want to draw the point. Press. The point isdrawn.

To continue to draw points, repeat step 2. To cancel PT.ON(,

pressM.

Drawing Points

DRAW POINTS

Menu

Drawing a Point

Directly on a

Graph

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Draw Operations 7-11

Procedures for using PT.OFF( (point off, DRAW POINTS, item

2) to turn off (erase) a point and PT.CHANGE( (point change,

DRAW POINTS, item 3) to toggle (reverse) a point on and off

are the same as forPT.ON(.

When you use these instructions from the Home screen or aprogram, you must specify the X-coordinate and the

Y-coordinate of the point as arguments for the instructions.

PT.ON( turns on the point at (X=X,Y=Y). PT.OFF( turns the

point off, and PT.CHANGE( toggles the point between on and

off.

PT.ON(X,Y)

PT.OFF(X,Y)

PT.CHANGE(X,Y)

PT.OFF(

PT.CHANGE(

From the HomeScreen or a

Program

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7-12 Draw Operations

All points, lines, and

TI-80

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